<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0201</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2004-03-14</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000943819</issuerCik>
        <issuerName>RESMED INC</issuerName>
        <issuerTradingSymbol>RMD</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001272012</rptOwnerCik>
            <rptOwnerName>EISEN PAUL</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>69 CARINDA DRIVE</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>GLENHAVEN NSW</rptOwnerCity>
            <rptOwnerState>C3</rptOwnerState>
            <rptOwnerZipCode>2156</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>Vice President, Europe &amp; Asia</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>ResMed Common Stock</value>
                <footnoteId id="F1"/>
            </securityTitle>
            <transactionDate>
                <value>2004-03-14</value>
                <footnoteId id="F2"/>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>S</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionTimeliness>
                <value></value>
            </transactionTimeliness>
            <transactionAmounts>
                <transactionShares>
                    <value>350</value>
                    <footnoteId id="F1"/>
                </transactionShares>
                <transactionPricePerShare>
                    <value>45.70</value>
                    <footnoteId id="F3"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>D</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>0</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>Spouse</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
    </nonDerivativeTable>

    <footnotes>
        <footnote id="F1">Ownership was held in the form of 3500 CDI's purchased on the Australian Stock Exchange which converts to 350 shares of RMD Common Stock on the NYSE</footnote>
        <footnote id="F2">Trade was executed on 3/15/2004 in Australia, which was 3/14/2004 in the US</footnote>
        <footnote id="F3">Share price was AUD 6.18 which converts to $45.70 US</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Paul Eisen</signatureName>
        <signatureDate>2004-03-16</signatureDate>
    </ownerSignature>
</ownershipDocument>

